1 . 已知函数
.
(1)求函数
在点
处的切线方程;
(2)求函数
的单调区间;
(3)若
为
的导函数,设
.证明:对任意
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103618ff62d78974e9aae017df9e37f1.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efea404ec4afc504335f713aa6ee5262.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73f42cbdc123e91143781b27161128e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a264e9065e45b524e7ad9f675619b98a.png)
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名校
2 . 已知函数
,
(1)当
时,求
在区间
上的值域;
(2)若
有两个不同的零点
,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e9f45f86ee4cac88d16435393c7cec.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7eccdc19dbe2b4c7a30878c054e8c7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29909a4fdb8764b59f28bb63ce8da9db.png)
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2024-01-15更新
|
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|
3卷引用:广西柳州市高级中学2024届高三上学期12月月考数学试题
名校
解题方法
3 . 已知函数
(其中
,
为自然对数的底数).
(1)若函数
存在极大值,且极大值不小于1,求a的取值范围;
(2)当
时,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb309d10861e722e604e4b2879b439d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f7f23e7f20dd8bc65a4967cd306782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351be5371313be5ad69de2a49838b5c2.png)
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4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e501c6bcd97cc8aa3cd5205eca3f50.png)
(1)若函数
在
时取得极值,求
的单调减区间;
(2)证明:当
时,函数
有零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e501c6bcd97cc8aa3cd5205eca3f50.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b8cbc6de04416d2b904fc0475227d4.png)
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2022-11-25更新
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2卷引用:广西柳州市民族高中2023届高三上学期11月模拟统考数学(文)试题
5 . 已知函数
.
(1)若
在
上是增函数,求实数
的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8163ef24d8945d690949e4a0a85077f8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f25bcb0e6fb29e378fd3de0cd26056.png)
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2022-09-01更新
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3卷引用:广西柳州高级中学、南宁市第二中学2023届高三上学期9月联考数学(文)试题
名校
解题方法
6 . 已知函数
.
(1)当
时,求
在区间
上的最小值;
(2)证明:
且
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6931daadb1ceeb1a3e02b5cbaaa84d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca6fbbd1a011b0a064a1261ff55a061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a37ed7d5bf043795fd8d9ba77092b81.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcab40166b46cd1f4b8d8c9a5c336af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
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2023-01-02更新
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5卷引用:广西柳州市2023届高三第三次模拟数学(理)试题
广西柳州市2023届高三第三次模拟数学(理)试题湖南省长沙市雅礼中学2022-2023学年高三上学期月考(五)数学试题江西省吉安市第三中学2023届高三下学期3月月考数学(文)试题(已下线)河南省信阳市信阳高级中学2024届高三上学期测试(四)数学试题湖南省长沙市宁乡市第一高级中学2021届高三第二次模拟考试数学试题
7 . 已知平面上动点Q(x,y)到F(0,1)的距离比Q(x,y)到直线
的距离小1,记动点Q(x,y)的轨迹为曲线C.
(1)求曲线C的方程.
(2)设点P的坐标为(0,-1),过点P作曲线C的切线,切点为A,若过点P的直线m与曲线C交于M,N两点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fec96b5e74f5c2915a1d34d0fdeb737.png)
(1)求曲线C的方程.
(2)设点P的坐标为(0,-1),过点P作曲线C的切线,切点为A,若过点P的直线m与曲线C交于M,N两点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766ab8e8f778cd4c40133eb04963425e.png)
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2022-07-05更新
|
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4卷引用:广西柳州市2023届新高三摸底考试数学(理)试题
8 . 已知函数
.
(1)讨论当
时,f(x)单调性.
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/399a442d81eae3a491134f130fff29c4.png)
(1)讨论当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4eae40ed82623efa520979b9b12066.png)
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2022-07-05更新
|
730次组卷
|
3卷引用:广西柳州市2023届新高三摸底考试数学(理)试题
解题方法
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bba37d87f9abd96d4cbaceba40a34c.png)
(1)当
时,求函数
的最大值;
(2)若函数
有两个极值点
,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bba37d87f9abd96d4cbaceba40a34c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e4b5aa14dd784603da386f58606359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d07f69976c70d36d185885e591ee34.png)
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名校
10 . 若
.
(1)当
,
时,讨论函数
的单调性;
(2)若
,且
有两个极值点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88e66a16aa8cb0ac264e28c80914bf1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d00e896ece0bec6845cdf25235bcbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39118ef6d6bc0d89b70197b20085c36.png)
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2022-03-31更新
|
1846次组卷
|
6卷引用:广西柳州市2022届高三第三次模拟考试数学(理)试题